2 Answers
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This isn't an easy one: collections can vary considerably in value according to the rarity and desirability of their component parts. There are several approaches you can take to valuing a collection, but it really depends on how much work you're prepared to put in.

Of course, the only true indicator of anything is the amount that someone is prepared to pay for it. However, as a lot of people are buying and selling LEGO, we can get a lot more specific than that.

The Stupidly Fancy Method

Now, at the extreme end of the spectrum, you could go to the trouble of cataloguing every component in the collection and coming up with a price for each piece - based on BrickLink or something similar. There are 3 problems with this approach:

Prices on BrickLink are a fair guide, but remember that these are selling prices, which may not match the price that someone is willing to spend. For common components the prices are probably about right, but for rarer ones the vendors may be asking unrealistic prices.

It isn't all about the parts. Complete sets may be worth more than their component parts, especially if boxes and instructions are present and in good condition. Mint, unopened sets are often worth more than opened sets, but how much more depends on the set.

For anything but the smallest collection, this approach is prohibitively time consuming for us mere mortals.

The Easy Way

At the other end of the spectrum is another approach: weigh the collection, and base the price on weight. People often sell by weight on eBay, so by looking at a few listings it is fairly easy to come up with a figure for price per kg (or lb). The problem with this is:

There is a fairly wide variation of prices on eBay.

It doesn't take into account complete sets, manuals etc.

Some parts are quite heavy - motors, weights etc.

This approach doesn't take into account the difference between collections with lots of small parts vs lots of larger ones.

Some parts are worth more because they're rare or particularly desirable, e.g. minifigs tend to be more desirable than regular bricks, star wars components are more desirable.

Despite these issues, this general approach seems to be fairly common on eBay. They might sell for more by parting-out, but the effort and time involved just isn't worth it.

You should be left with a pile of bricks. Pull out all the minifigs (don't worry too much if you miss a few, and ignore their accessories) unless they're already holding them.

Weigh the remaining loose bricks, and use your price / kg to value them. If you think there is non-LEGO in there (megablocks etc.) either pull them out or reduce your price a bit.

Weigh the complete sets. Use your price / kg to value them and then add a % based on how desirable you think the sets are. Castle, train, space (inc. StarWars), pirate and technic tend to be worth a bit more.

Assign a nominal value to each minifig. Regular city people are worth quite a bit less than "interesting" figs. Starwars are favourite, followed by other "fancy" ones. (If I were selling, I'd probably sell the figs in separate bundles).

Add this lot up.

Compare the difference between the guess you made in 0 and the answer you got in 7, and pick a price somewhere in between.

Of course, if I were buying I'd knock 20% off this price and insist that the seller do the same!

Notes on Pricing

When setting a price, consider the following general rules:

Although the age and rarity of a set or component has some relation to its desirability, they are not the most important part of price.

Quality of the parts matters a lot. Scratches or other marks lower price considerably. For example, I've got some old bricks from the 60s that are really poor for building because they're not made from the same plastic as newer bricks. As a result, people don't seem to want them, despite their relative age.

"Cuteness" of models matters a lot. Some of my oldest sets are quite rare, but they're also quite boring (e.g. sets of roof tiles). As a result they're no where near as valuable as a relatively common but fun set from the same era.

People like figs, so the pre-minifig era sets are not so desirable.

Many buyers like sets from their childhood, so nice space-themed sets from the late 70s - early 90s generally do well on the second-user market.

While this may not help you ascertain the value of someone else's collection you intend to buy or make an offer on, I'll add this for others who may want to know what their own collection is worth - using the Peeron website (www.peeron.com), you can work out the RRP of your own collection. Simply enter the set numbers into their database and Peeron will tally them up for you. As an example, here is what Peeron estimates my collection at:

Totals: 410 Sets (361 unique), 82,912 Parts, $7,249.10, 634 Minifigs.

Couldn't be easier, but you'll need a pretty comprehensive knowledge of your collected sets - it gets more complicated if you have a lot of loose parts bought or gathered outside of official sets.

Whilst this is useful information in its own right (I must admit I had no idea ths facility existed), you should be aware that the RRP of a set and its resale value can be quite different. An extreme exmple is 10179-1: Millennium Falcon. Its RRP was $500, but it can go for several times that on the second hand market (the cheapest sealed one on Bricklink is offered for about $1,700 a I write. No guarantee it will sell at that price, but still).
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KramiiSep 15 '13 at 4:02

Correct, but the RRP is a good median estimate for what one might consider their entire collection worth. Ultimately it comes down to having an in-depth knowledge of one's collected sets before estimating what the total sale value might be. It is worth mentioning that if one was to sell an entire collection in bulk, it's reasonable to expect that it would not fetch as high a price as it might if it was sold either in parts or per set. The key here is 'used'; it will never fetch the same price as 'new' so a buyer may likely negotiate a better sale price for a bulk collection of used LEGO.
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VeeSep 15 '13 at 11:00